First, the DUT is in the positive feedback because this way you have an inverting and a non-inverting gain in the loop, so that multiplying them you obtain an overall negative loop gain.
Second, the gain is 1000 because Vin of DUT is Vos*50/(50K+50), so if you consider that V+ of the DUT should be 0, there is only the offset applied, so the feedback forces the output to be 1k times the offset voltage.
I think that you can look at the output this way: suppose that the situation is the one described, and you have a 500uV DUT offset and so 500mV output voltage.
Now, if you try to perturb the Servo Input, the feedback forces the output of the DUT to be almost the same of Servo Input, restoring the same Output voltage.
Note: Voff is the conventional name for input offset voltage, while Vos is the output voltage with Voff applied at the input pins.
Best Answer
Yup. If you look at Figure 2 of the data sheet, it shows a nominal maximum for +/- 5 volt supplies to be 6 volts pk-pk. In other words, about +/- 3 volts, and you're getting -3. Just about what you'd expect.
The positive side is doing better than expected, but that's just an unexpected bonus.
TL;DR - You should never count on getting +/- 4.1 with your power supply and this op amp.